Investigação numérica da convecção natural de fluido de Bingham em cavidade fechada preenchida com meio poroso

Abstract

In the present study is investigated numerically the natural convection process of fluid with yield stress modeled as Bingham fluid in closed cavities filled with porous medium.The problem is solved as two-dimensional laminar in steady state with differentially heated vertical walls and adiabatic horizontal surfaces. In order to investigate the effects of some significant parameters describing the flow field and heat transfer, the Prandtl number is fixed as 500, the number of solid blocks within the cavity is set to range as 16,36 e 64, Rayleigh number is valued as 10 4 <= Ra <= 10 7 , the Bingham number from 0,001 to 1 and two porosity values for the porous medium, Φ = 0,36 e 0,64 and 0,64, are used. As the Rayleigh number increases, the average Nusselt number increases significantly. However, the effects are less significant for Bingham fluid with higher degree of viscoplasticity. For high Bingham numbers, the Nusselt number decreases to a limit value, which depends on the ratio fluid and solid of thermal conductivities, the number of blocks near the walls, and the porosity, where this value characterizes heat transfer purely by conduction. Results are presented in the form of streamlines, isotherms, velocity and dimensionless temperature in the mean horizontal plane, local Nusselt number and the average Nusselt number in the heated wall. With the increase in the number of blocks and the decrease in porosity, a pattern is observed in the appearance of unyielded regions within the cavity. The influence of nondimensional parameters (Rayleigh and Bingham numbers) is presented in diagrams that allow for the observation of the region where the fluid is static or moving. Finally, correlations for the maximum Bingham number and average Nusselt in the heated wall are obtained for each geometry.